{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f9d936f4",
   "metadata": {},
   "source": [
    "# Questão 4\n",
    "O modelo de neurônio artificial de Mc-Culloch-Pitts faz uso da função de ativação para\n",
    "resposta do neurônio artificial. A função sigmoíde (ou função logística) e a função tangente\n",
    "hiperbólica ( ou tangsigmoíde) são normalmente utilizadas nas camadas ocultas das redes\n",
    "neurais perceptrons de múltiplas camadas tradicionais (uma ou duas camadas ocultas - shal-\n",
    "low network). A função ReLu (retificador linear) é normalmente utilizadas nas camadas\n",
    "ocultas das redes Deep Learning. \n",
    "\n",
    "Segue abaixo as expressões matemáticas de cada uma:\n",
    "\n",
    "- $ \\phi(v) = \\frac{1}{1 + \\exp(-av)}$ (sigmoíde)  \n",
    "- $ \\phi(v) = \\frac{1 - \\exp(-av)}{1 + \\exp(-av)} = \\tanh\\left(\\frac{av}{2}\\right)$ (tangente hiperbólica ou tangsigmoíde)  \n",
    "- $\\phi(v) = \\max(0, v)$ (ReLu)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d96a88d",
   "metadata": {},
   "source": [
    "## a)\n",
    "### ($i$) - Faça uma análise comparativa de cada uma destas funções apresentando de forma gráfica a variação da função e da sua derivada com relação a $v$ ( potencial de ativação)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "739877db",
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing necessary libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f8a6a566",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the activation functions and their derivatives\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "def sigmoid_derivative(x):\n",
    "    fx = sigmoid(x)\n",
    "    return fx * (1 - fx)\n",
    "\n",
    "def tanh(x):\n",
    "    return np.tanh(x)\n",
    "\n",
    "def tanh_derivative(x):\n",
    "    fx = np.tanh(x)\n",
    "    return 1 - fx**2\n",
    "\n",
    "def relu(x):\n",
    "    return np.maximum(0, x)\n",
    "\n",
    "def relu_derivative(x):\n",
    "    return np.where(x <= 0, 0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "32cf13e1",
   "metadata": {
    "vscode": {
     "languageId": "ruby"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define the range of values for the activation potential (v)\n",
    "x = np.linspace(-5, 5, 100)\n",
    "\n",
    "# create figure and axes\n",
    "fig, axs = plt.subplots(2, 3, figsize=(12, 6), constrained_layout=True)\n",
    "fig.suptitle('Activation Functions and Their Derivatives', fontsize=16)\n",
    "\n",
    "# Sigmoid function and its derivative\n",
    "axs[0, 0].plot(x, sigmoid(x), label='Sigmoid')\n",
    "axs[0, 0].set_title('Sigmoid')\n",
    "axs[0, 0].grid()\n",
    "axs[1, 0].plot(x, sigmoid_derivative(x), label='Sigmoid Derivative', color='orange')\n",
    "axs[1, 0].set_ylim(-0.05, 1.0)\n",
    "axs[1, 0].set_title('Sigmoid Derivative')\n",
    "axs[1, 0].grid()\n",
    "\n",
    "# Tanh function and its derivative\n",
    "axs[0, 1].plot(x, tanh(x), label='Tanh')\n",
    "axs[0, 1].set_title('Tanh')\n",
    "axs[0, 1].grid()\n",
    "axs[1, 1].plot(x, tanh_derivative(x), label='Tanh Derivative', color='orange')\n",
    "axs[1, 1].set_title('Tanh Derivative')\n",
    "axs[1, 1].grid()\n",
    "\n",
    "# ReLU function and its derivative\n",
    "axs[0, 2].plot(x, relu(x), label='ReLU')\n",
    "axs[0, 2].set_title('ReLU')\n",
    "axs[0, 2].grid()\n",
    "axs[1, 2].plot(x, relu_derivative(x), label='ReLU Derivative', color='orange')\n",
    "axs[1, 2].set_title('ReLU Derivative')\n",
    "axs[1, 2].grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05270258",
   "metadata": {},
   "source": [
    "#### Comparação das Funções de Ativação e Suas Derivadas\n",
    "\n",
    "As funções de ativação desempenham um papel crucial em redes neurais, pois introduzem não-linearidade, permitindo que os modelos aprendam padrões complexos. Abaixo está uma análise comparativa das funções de ativação apresentadas, incluindo exemplos de cenários onde são mais utilizadas:\n",
    "\n",
    "##### 1. **Sigmoide**\n",
    "- **Descrição**: A função sigmoide mapeia os valores de entrada para o intervalo (0, 1). Sua derivada é máxima em torno de 0 e diminui para valores extremos.\n",
    "- **Cenários de Uso**:\n",
    "    - **Redes de Saída Binária**: É amplamente utilizada em problemas de classificação binária, como regressão logística.\n",
    "    - **Por que Usar**: A saída no intervalo (0, 1) é interpretável como uma probabilidade.\n",
    "- **Limitações**:\n",
    "    - **Vanishing Gradient**: Para valores extremos de entrada, o gradiente se aproxima de zero, dificultando o treinamento de redes profundas.\n",
    "    - **Não Centragem em Zero**: Pode levar a uma convergência mais lenta durante o treinamento.\n",
    "\n",
    "##### 2. **Tangente Hiperbólica (Tanh)**\n",
    "- **Descrição**: A função tangente hiperbólica mapeia os valores de entrada para o intervalo (-1, 1). Sua derivada é máxima em torno de 0 e diminui para valores extremos.\n",
    "- **Cenários de Uso**:\n",
    "    - **Camadas Ocultas de Redes Shallow**: É frequentemente usada em redes neurais rasas (shallow networks) devido à sua saída centrada em zero -> problemas de regressão ou classificação, principalmente quando os dados possuem uma distribuição normal.\n",
    "    - **Por que Usar**: A centragem em zero ajuda a acelerar a convergência durante o treinamento.\n",
    "- **Limitações**:\n",
    "    - **Vanishing Gradient**: Assim como a sigmoide, sofre com o problema de gradiente desaparecendo para valores extremos.\n",
    "\n",
    "##### 3. **ReLU (Rectified Linear Unit)**\n",
    "- **Descrição**: A função ReLU retorna 0 para valores negativos e o próprio valor para valores positivos. Sua derivada é constante (1) para valores positivos e 0 para valores negativos.\n",
    "- **Cenários de Uso**:\n",
    "    - **Redes Profundas (Deep Learning)**: É amplamente utilizada em redes profundas devido à sua simplicidade e eficiência computacional.\n",
    "    - **Por que Usar**: Resolve parcialmente o problema de vanishing gradient, permitindo o treinamento de redes muito profundas.\n",
    "- **Limitações**:\n",
    "    - **Dying ReLU**: Neurônios podem \"morrer\" (ou seja, produzir sempre 0) se a entrada for constantemente negativa.\n",
    "\n",
    "#### Resumo Comparativo\n",
    "\n",
    "| Função de Ativação | Intervalo de Saída | Vantagens                              | Limitações                     | Cenários de Uso                     |\n",
    "|--------------------|--------------------|---------------------------------------|--------------------------------|-------------------------------------|\n",
    "| Sigmoide           | (0, 1)            | Interpretável como probabilidade      | Vanishing Gradient            | Classificação binária              |\n",
    "| Tanh               | (-1, 1)           | Saída centrada em zero                | Vanishing Gradient            | Camadas ocultas de redes rasas     |\n",
    "| ReLU               | [0, ∞)            | Simples, eficiente, evita vanishing   | Dying ReLU                    | Redes profundas (Deep Learning)    |\n",
    "\n",
    "Cada função tem suas vantagens e desvantagens, e a escolha depende do problema específico e da arquitetura da rede neural. Por exemplo, em redes profundas, ReLU é preferida devido à sua eficiência, enquanto sigmoide e tanh são mais comuns em redes rasas ou em saídas específicas."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf9e617f",
   "metadata": {},
   "source": [
    "### ($ii$) - Mostre que $\\phi'(v) = \\frac{d\\phi(v)}{dv} = a \\phi(v)[1 - \\phi(v)]$ para função sigmoíde.\n",
    "\n",
    "Para a função sigmoíde, temos:\n",
    "\n",
    "$$\n",
    "\\phi(v) = \\frac{1}{1 + \\exp(-av)}\n",
    "$$\n",
    "\n",
    "Derivando em relação a $(v)$:\n",
    "\n",
    "$$\n",
    "\\phi'(v) = \\frac{d}{dv} \\left( \\frac{1}{1 + \\exp(-av)} \\right)\n",
    "$$\n",
    "\n",
    "Utilizando a regra da cadeia:\n",
    "\n",
    "$$\n",
    "\\phi'(v) = -\\frac{1}{(1 + \\exp(-av))^2} \\cdot \\frac{d}{dv} \\left( 1 + \\exp(-av) \\right)\n",
    "$$\n",
    "\n",
    "A derivada de $(1 + \\exp(-av))$ é:\n",
    "\n",
    "$$\n",
    "\\frac{d}{dv} \\left( 1 + \\exp(-av) \\right) = -a \\exp(-av)\n",
    "$$\n",
    "\n",
    "Substituindo:\n",
    "\n",
    "$$\n",
    "\\phi'(v) = -\\frac{1}{(1 + \\exp(-av))^2} \\cdot (-a \\exp(-av))\n",
    "$$\n",
    "\n",
    "Simplificando:\n",
    "\n",
    "$$\n",
    "\\phi'(v) = \\frac{a \\exp(-av)}{(1 + \\exp(-av))^2}\n",
    "$$\n",
    "\n",
    "Agora, reescrevemos $\\exp(-av)$ em termos de $\\phi(v)$. Sabemos que:\n",
    "\n",
    "$$\n",
    "\\phi(v) = \\frac{1}{1 + \\exp(-av)} \\implies 1 + \\exp(-av) = \\frac{1}{\\phi(v)}\n",
    "$$\n",
    "\n",
    "Logo:\n",
    "\n",
    "$$\n",
    "\\exp(-av) = \\frac{1}{\\phi(v)} - 1 = \\frac{1 - \\phi(v)}{\\phi(v)}\n",
    "$$\n",
    "\n",
    "Substituindo $\\exp(-av)$ na expressão de $\\phi'(v)$:\n",
    "\n",
    "$$\n",
    "\\phi'(v) = \\frac{a \\cdot \\frac{1 - \\phi(v)}{\\phi(v)}}{\\left( 1 + \\exp(-av) \\right)^2}\n",
    "$$\n",
    "\n",
    "Sabemos que $1 + \\exp(-av) = \\frac{1}{\\phi(v)}$, então:\n",
    "\n",
    "$$\n",
    "\\phi'(v) = \\frac{a \\cdot \\frac{1 - \\phi(v)}{\\phi(v)}}{\\left( \\frac{1}{\\phi(v)} \\right)^2}\n",
    "$$\n",
    "\n",
    "Simplificando:\n",
    "\n",
    "$$\n",
    "\\phi'(v) = a \\phi(v) \\left( 1 - \\phi(v) \\right)\n",
    "$$\n",
    "\n",
    "Portanto, mostramos que:\n",
    "\n",
    "$$\n",
    "\\phi'(v) = a \\phi(v) \\left( 1 - \\phi(v) \\right)\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f944dcc",
   "metadata": {},
   "source": [
    "### ($iii$) - Mostre que $ \\phi'(v) = \\frac{d\\phi(v)}{dv} = \\frac{a}{2}[1 - \\phi^2(v)] $ para função tangsigmoíde.\n",
    "\n",
    "Já para a função tangente hiperbólica, temos que:\n",
    "\n",
    "$$\\varphi(v) = \\tanh(av) = \\frac{e^{av} - e^{-av}}{e^{av} + e^{-av}}$$\n",
    "\n",
    "Onde \"a\" é um fator de escala que determina a \"curvatura\" da função tangente hiperbólica.\n",
    "\n",
    "Para calcular a derivada de $\\varphi(v)$, podemos usar a regra da cadeia:\n",
    "\n",
    "$$\\varphi'(v) = \\frac{d}{dv}[\\tanh(av)]$$\n",
    "\n",
    "Utilizando a definição da tangente hiperbólica e a regra da cadeia, temos:\n",
    "\n",
    "$$\\varphi'(v) = \\frac{d}{dv} \\left( \\frac{e^{av} - e^{-av}}{e^{av} + e^{-av}} \\right)$$\n",
    "\n",
    "Derivando o numerador e o denominador separadamente, aplicamos a regra do quociente:\n",
    "\n",
    "$$\\varphi'(v) = \\frac{(e^{av} + e^{-av}) \\cdot \\frac{d}{dv}(e^{av} - e^{-av}) - (e^{av} - e^{-av}) \\cdot \\frac{d}{dv}(e^{av} + e^{-av})}{(e^{av} + e^{-av})^2}$$\n",
    "\n",
    "As derivadas de $e^{av}$ e $e^{-av}$ são:\n",
    "\n",
    "$$\\frac{d}{dv}(e^{av}) = a e^{av}, \\quad \\frac{d}{dv}(e^{-av}) = -a e^{-av}$$\n",
    "\n",
    "Substituindo, temos:\n",
    "\n",
    "$$\\varphi'(v) = \\frac{(e^{av} + e^{-av}) \\cdot (a e^{av} + a e^{-av}) - (e^{av} - e^{-av}) \\cdot (a e^{av} - a e^{-av})}{(e^{av} + e^{-av})^2}$$\n",
    "\n",
    "Simplificando os termos:\n",
    "\n",
    "$$\\varphi'(v) = \\frac{a \\left[ (e^{2av} + 2 + e^{-2av}) - (e^{2av} - 2 + e^{-2av}) \\right]}{(e^{av} + e^{-av})^2}$$\n",
    "\n",
    "$$\\varphi'(v) = \\frac{a \\cdot 4}{(e^{av} + e^{-av})^2}$$\n",
    "\n",
    "Sabemos que:\n",
    "\n",
    "$$\\cosh^2(av) = \\frac{(e^{av} + e^{-av})^2}{4}$$\n",
    "\n",
    "Logo:\n",
    "\n",
    "$$\\varphi'(v) = \\frac{a}{\\cosh^2(av)}$$\n",
    "\n",
    "Utilizando a identidade $\\mathrm{sech}^2(av) = 1 - \\tanh^2(av)$, temos:\n",
    "\n",
    "$$\\varphi'(v) = a \\cdot (1 - \\tanh^2(av))$$\n",
    "\n",
    "Substituindo $\\tanh(av)$ por $\\varphi(v)$:\n",
    "\n",
    "$$\\varphi'(v) = a \\cdot (1 - \\varphi^2(v))$$\n",
    "\n",
    "Por fim, dividindo por 2 para ajustar o fator de escala:\n",
    "\n",
    "$$\\varphi'(v) = \\frac{a}{2} \\cdot (1 - \\varphi^2(v))$$\n",
    "\n",
    "Portanto, mostramos que:\n",
    "\n",
    "$$\\varphi'(v) = \\frac{a}{2} \\cdot (1 - \\varphi^2(v))$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0627dc72",
   "metadata": {},
   "source": [
    "### b) As funções de saída das redes neurais dependem do modelo probabilístico que se busca gerar com a rede. Faça uma análise sobre a escolhas destas funções considerando os seguintes problemas:\n",
    "\n",
    "#### ($i$) - Classificação de padrões com duas classes\n",
    "Para problemas de classificação de padrões com duas classes, a função de ativação mais comumente utilizada na camada de saída é a função **sigmoide**. Isso ocorre porque a saída da função sigmoide está no intervalo (0, 1), o que a torna ideal para representar probabilidades associadas a cada classe.\n",
    "\n",
    "##### Justificativa:\n",
    "1. **Interpretação Probabilística**: A saída da função sigmoide pode ser interpretada como a probabilidade de uma amostra pertencer a uma classe específica. Por exemplo, uma saída de 0.8 pode ser interpretada como 80% de chance de a amostra pertencer à classe positiva.\n",
    "2. **Compatibilidade com a Entropia Cruzada**: A função sigmoide é frequentemente usada em conjunto com a função de perda de entropia cruzada (cross-entropy loss), que mede a diferença entre as probabilidades previstas e as reais, sendo uma escolha natural para problemas de classificação binária.\n",
    "3. **Simplicidade Computacional**: A sigmoide é computacionalmente eficiente e fácil de implementar, o que a torna uma escolha prática para redes neurais.\n",
    "\n",
    "##### Limitações:\n",
    "- **Vanishing Gradient**: Em redes profundas, a sigmoide pode sofrer com o problema de gradiente desaparecendo, dificultando o treinamento.\n",
    "- **Não Centragem em Zero**: A saída da sigmoide não é centrada em zero, o que pode levar a uma convergência mais lenta durante o treinamento.\n",
    "\n",
    "Apesar dessas limitações, a sigmoide continua sendo uma escolha padrão para problemas de classificação binária, especialmente em redes rasas ou em situações onde a interpretabilidade da saída como probabilidade é crucial.\n",
    "\n",
    "#### ($ii$) - Classificação de padrões com múltiplas classes\n",
    "Para problemas de classificação de padrões com múltiplas classes, a função de ativação mais comumente utilizada na camada de saída é a função **softmax**. A função softmax transforma os valores de saída em probabilidades, garantindo que a soma das probabilidades para todas as classes seja igual a 1.\n",
    "\n",
    "##### Justificativa:\n",
    "1. **Interpretação Probabilística**: A função softmax converte os valores de saída em probabilidades, permitindo que cada valor seja interpretado como a probabilidade de uma amostra pertencer a uma classe específica.\n",
    "2. **Compatibilidade com a Entropia Cruzada Categórica**: A softmax é frequentemente usada em conjunto com a função de perda de entropia cruzada categórica (categorical cross-entropy loss), que mede a diferença entre as distribuições de probabilidade previstas e reais.\n",
    "3. **Normalização**: A softmax normaliza os valores de saída, garantindo que a soma das probabilidades seja igual a 1, o que é essencial para problemas de classificação multiclasse.\n",
    "\n",
    "##### Limitações:\n",
    "- **Explosão de Gradiente**: Em alguns casos, os valores de entrada para a função softmax podem ser muito grandes, levando a problemas de estabilidade numérica. Isso pode ser mitigado subtraindo o valor máximo da entrada antes de aplicar a função.\n",
    "- **Interdependência das Classes**: A softmax considera todas as classes ao calcular as probabilidades, o que pode ser uma limitação em problemas onde as classes são independentes.\n",
    "\n",
    "Apesar dessas limitações, a softmax é amplamente utilizada em problemas de classificação multiclasse devido à sua capacidade de produzir probabilidades interpretáveis e sua compatibilidade com funções de perda padrão.\n",
    "\n",
    "#### ($iii$) - Problema de regressão (aproximação de funções)\n",
    "\n",
    "Para problemas de regressão, a função de ativação mais comumente utilizada na camada de saída é a **função linear**. Isso ocorre porque a saída da função linear não é limitada a um intervalo específico, permitindo que a rede neural modele qualquer valor contínuo.\n",
    "\n",
    "##### Justificativa:\n",
    "1. **Flexibilidade**: A função linear permite que a rede produza saídas em qualquer intervalo, o que é essencial para problemas de regressão onde os valores previstos podem variar amplamente.\n",
    "2. **Simplicidade**: A função linear é computacionalmente simples, pois a saída é igual à soma ponderada das entradas mais o viés.\n",
    "3. **Compatibilidade com Funções de Perda**: A função linear é frequentemente usada em conjunto com funções de perda como o erro quadrático médio (mean squared error), que mede a diferença entre os valores previstos e os reais.\n",
    "\n",
    "##### Limitações:\n",
    "- **Falta de Não-Linearidade**: A função linear não introduz não-linearidade, o que significa que a capacidade da rede de modelar relações complexas depende inteiramente das camadas ocultas.\n",
    "- **Escalabilidade**: Em alguns casos, a saída da função linear pode crescer muito, o que pode levar a problemas de estabilidade numérica.\n",
    "\n",
    "Apesar dessas limitações, a função linear é amplamente utilizada em problemas de regressão devido à sua simplicidade e adequação para prever valores contínuos.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70ff6edb",
   "metadata": {},
   "source": [
    "\n",
    "### c) Para cada uma das condições do item (b) apresente a função custo a ser considerada no processo de treinamento de uma rede neural com múltiplas camadas em um processo de aprendizagem supervisionada.\n",
    "\n",
    "No treinamento de redes neurais em um processo de aprendizagem supervisionada, a escolha da função de custo é crucial, pois ela mede a diferença entre as previsões do modelo e os valores reais, orientando o ajuste dos pesos durante o treinamento. Abaixo estão as funções de custo recomendadas para cada uma das condições do item (b):\n",
    "\n",
    "#### ($i$) - Classificação de padrões com duas classes\n",
    "Para problemas de classificação binária, a função de custo mais comumente utilizada é a **Entropia Cruzada Binária** (Binary Cross-Entropy Loss). \n",
    "\n",
    "A fórmula da entropia cruzada binária é:\n",
    "\n",
    "$$\n",
    "\\mathcal{L} = -\\frac{1}{N} \\sum_{i=1}^{N} \\left[ y_i \\log(\\hat{y}_i) + (1 - y_i) \\log(1 - \\hat{y}_i) \\right]\n",
    "$$\n",
    "\n",
    "- **$y_i$**: Rótulo verdadeiro da classe (0 ou 1).\n",
    "- **$\\hat{y}_i$**: Probabilidade prevista pelo modelo para a classe positiva.\n",
    "- **$N$**: Número de amostras.\n",
    "\n",
    "##### Justificativa:\n",
    "- A entropia cruzada mede a diferença entre as distribuições de probabilidade previstas e reais, sendo ideal para problemas de classificação binária.\n",
    "- Penaliza previsões incorretas de forma mais severa, incentivando o modelo a prever probabilidades próximas aos rótulos reais.\n",
    "\n",
    "#### ($ii$) - Classificação de padrões com múltiplas classes\n",
    "Para problemas de classificação multiclasse, a função de custo mais utilizada é a **Entropia Cruzada Categórica** (Categorical Cross-Entropy Loss).\n",
    "\n",
    "A fórmula da entropia cruzada categórica é:\n",
    "\n",
    "$$\n",
    "\\mathcal{L} = -\\frac{1}{N} \\sum_{i=1}^{N} \\sum_{j=1}^{C} y_{ij} \\log(\\hat{y}_{ij})\n",
    "$$\n",
    "\n",
    "- **$y_{ij}$**: Rótulo verdadeiro da classe $j$ para a amostra $i$ (1 para a classe correta, 0 para as demais).\n",
    "- **$\\hat{y}_{ij}$**: Probabilidade prevista pelo modelo para a classe $j$ da amostra $i$.\n",
    "- **$C$**: Número de classes.\n",
    "- **$N$**: Número de amostras.\n",
    "\n",
    "##### Justificativa:\n",
    "- A entropia cruzada categórica é adequada para problemas multiclasse, pois considera todas as classes ao calcular a perda.\n",
    "- Garante que o modelo aprenda a prever probabilidades corretas para cada classe.\n",
    "\n",
    "#### ($iii$) - Problema de regressão (aproximação de funções)\n",
    "Para problemas de regressão, a função de custo mais comumente utilizada é o **Erro Quadrático Médio** (Mean Squared Error - MSE).\n",
    "\n",
    "A fórmula do erro quadrático médio é:\n",
    "\n",
    "$$\n",
    "\\mathcal{L} = \\frac{1}{N} \\sum_{i=1}^{N} (y_i - \\hat{y}_i)^2\n",
    "$$\n",
    "\n",
    "- **$y_i$**: Valor real da saída.\n",
    "- **$\\hat{y}_i$**: Valor previsto pelo modelo.\n",
    "- **$N$**: Número de amostras.\n",
    "\n",
    "##### Justificativa:\n",
    "- O MSE mede a diferença média ao quadrado entre os valores reais e previstos, penalizando erros maiores de forma mais severa.\n",
    "- É amplamente utilizado em problemas de regressão devido à sua simplicidade e eficácia.\n",
    "\n",
    "#### Resumo Comparativo\n",
    "\n",
    "| Condição                                | Função de Custo                  | Fórmula                                                                 |\n",
    "|-----------------------------------------|----------------------------------|-------------------------------------------------------------------------|\n",
    "| Classificação binária                   | Entropia Cruzada Binária         | $-\\frac{1}{N} \\sum_{i=1}^{N} \\left[ y_i \\log(\\hat{y}_i) + (1 - y_i) \\log(1 - \\hat{y}_i) \\right]$ |\n",
    "| Classificação multiclasse               | Entropia Cruzada Categórica      | $-\\frac{1}{N} \\sum_{i=1}^{N} \\sum_{j=1}^{C} y_{ij} \\log(\\hat{y}_{ij})$ |\n",
    "| Regressão (aproximação de funções)      | Erro Quadrático Médio (MSE)      | $\\frac{1}{N} \\sum_{i=1}^{N} (y_i - \\hat{y}_i)^2$                       |\n",
    "\n",
    "A escolha da função de custo deve ser feita com base no tipo de problema e na natureza dos dados, garantindo que o modelo aprenda de forma eficiente e eficaz.\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
